If you allowed utility functions to condition on the entire history (observation, actions and any changes induced in the agent by the environment), you could describe agent preferences, but at that point you lose all the nice properties of EU maximisation.
You’re no longer prescribing how a rational agent should behave and the utility function no longer constrains agent behaviour (any action is EU maximisation). Whatever action the agent takes becomes the action with the highest utility.
Utility functions that condition on an agent’s history are IMO not useful for theories of normative decision making or rationality. They become a purely descriptive artifact.
If anyone can point me to what kinds of preferences are supposed to be outlawed by this “insist on being a utility function” I would benefit from that.
They say that you are allowed to define utility functions however you want, but that doing so broadly enough can mean that “X is behaving according to a utility function” is no longer anticipation-constraining, so you can’t infer anything new about X from it.
If you allowed utility functions to condition on the entire history (observation, actions and any changes induced in the agent by the environment), you could describe agent preferences, but at that point you lose all the nice properties of EU maximisation.
You’re no longer prescribing how a rational agent should behave and the utility function no longer constrains agent behaviour (any action is EU maximisation). Whatever action the agent takes becomes the action with the highest utility.
Utility functions that condition on an agent’s history are IMO not useful for theories of normative decision making or rationality. They become a purely descriptive artifact.
If anyone can point me to what kinds of preferences are supposed to be outlawed by this “insist on being a utility function” I would benefit from that.
See: Why Subagents? for a treatment of how stateless utility functions fail to capture inexploitable path dependent preferences.
This and this are decent discussions.
So it seems i have understood correctly and both of those say that nothing is outlawed (and that incoherence is broken as a concept).
They say that you are allowed to define utility functions however you want, but that doing so broadly enough can mean that “X is behaving according to a utility function” is no longer anticipation-constraining, so you can’t infer anything new about X from it.